Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Sagman, Nathaniel"'
Autor:
Emam, Christian El, Sagman, Nathaniel
We prove that, on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component, the Goldman symplectic form and the Labourie-Loftin complex structure are compatible and together determine a (mapping class group invariant) pseudo-K\"ahler structure.
Externí odkaz:
http://arxiv.org/abs/2411.02350
Autor:
Sagman, Nathaniel, Tošić, Ognjen
We develop a Lie-theoretic perspective on Hitchin's equations for cyclic $G$-Higgs bundles, which we use to study analytic and geometric properties of harmonic maps. Among other things, we prove Dai-Li's conjecture on the monotonicity of the energy d
Externí odkaz:
http://arxiv.org/abs/2410.20853
Autor:
Emam, Christian El, Sagman, Nathaniel
We prove that, given a path of Beltrami differentials on $\mathbb C$ that live in and vary holomorphically in the Sobolev space $W^{l,\infty}_{loc}(\Omega)$ of an open subset $\Omega\subset \mathbb C$, the canonical solutions to the Beltrami equation
Externí odkaz:
http://arxiv.org/abs/2410.06175
Autor:
Emam, Christian El, Sagman, Nathaniel
For $S$ a closed surface of genus at least $2$, let $\mathrm{Hit}_3(S)$ be the Hitchin component of representations to $\mathrm{SL}(3,\mathbb{R}),$ equipped with the Labourie-Loftin complex structure. We construct a mapping class group equivariant ho
Externí odkaz:
http://arxiv.org/abs/2406.15287
Autor:
Sagman, Nathaniel
We prove that for any two Riemannian metrics $\sigma_1, \sigma_2$ on the unit disk, a homeomorphism $\partial\mathbb{D}\to\partial\mathbb{D}$ extends to at most one quasiconformal minimal diffeomorphism $(\mathbb{D},\sigma_1)\to (\mathbb{D},\sigma_2)
Externí odkaz:
http://arxiv.org/abs/2310.00778
Autor:
Sagman, Nathaniel
With respect to every Riemannian metric, the Teichm\"uller metric, and the Thurston metric on Teichm\"uller space, we show that there exist measured foliations on surfaces whose extremal length functions are not convex. The construction uses harmonic
Externí odkaz:
http://arxiv.org/abs/2303.04471
Autor:
Markovic, Vladimir, Sagman, Nathaniel
We establish the new main inequality as a minimizing criterion for minimal maps to products of $\mathbb{R}$-trees, and the infinitesimal new main inequality as a stability criterion for minimal maps to $\mathbb{R}^n$. Along the way, we develop a new
Externí odkaz:
http://arxiv.org/abs/2301.00249
Autor:
Sagman, Nathaniel Levi
Harmonic maps are fundamental objects in differential geometry. They play an important role in studying deformations of geometric structures and in various rigidity problems. In this thesis, we present three projects, all of which involve harmonic ma
Autor:
Sagman, Nathaniel, Smillie, Peter
We prove that if $\Sigma$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space $N$, then there exists a Hitchin representation $\rho:\pi_1(\Sigm
Externí odkaz:
http://arxiv.org/abs/2208.04885
We prove that every unstable equivariant minimal surface in $\mathbb{R}^n$ produces a maximal representation of a surface group into $\prod_{i=1}^n\textrm{PSL}(2,\mathbb{R})$ together with an unstable minimal surface in the corresponding product of c
Externí odkaz:
http://arxiv.org/abs/2206.02938